What is a three-dimensional array?

A three-dimensional array is a static structure holding elements of one type that are located by three subscripts, so it behaves as a stack of two-dimensional tables.

How many elements does an array declared with bounds 0 to 2, 0 to 3 and 0 to 4 hold?

It holds 3 × 4 × 5 = 60 elements.

How is a single element of a three-dimensional array referred to in a program?

It is referred to by the array name followed by all three subscripts, such as sales[2][1][4].

Explain how a colour image is held in a three-dimensional array.

The first two subscripts give the row and column of the pixel and the third selects the red, green or blue component of that pixel.

WJEC A-Level Computer Science 601-5345-3

Hardware: Architecture, Memory and Storage

Topic overview Components of a computer system and how they connect Von Neumann architecture and the CPU The fetch-execute cycle Memory and caching Parallel processing Input and output devices and their uses Secondary storage, fragmentation and defragmentation

Networks and Data Transmission

Topic overview Serial and parallel transmission Simplex, half duplex and full duplex Multiplexing and switching Packets and the TCP/IP protocol stack Networks, standards and protocols Collisions and shared media Routing, addressing and the internet

Logic Gates and Boolean Algebra

Topic overview Logic gates and their truth tables Boolean notation and expressions Building and reading truth tables Boolean identities and rules Simplifying Boolean expressions De Morgan's laws Masking and clearing registers

Data Representation and Data Types

Topic overview Bits, bytes and words The binary number system Hexadecimal notation Character sets and storing characters Primitive data types and storage requirements Binary arithmetic and negative numbers Real numbers, truncation and rounding

Data Structures

Topic overview Data structures and data types One-dimensional arrays Two-dimensional arrays Manipulating arrays Records and fields Arrays of records Choosing a data structure

Organisation of Data: Files and Records

Topic overview Files, records and fields Fixed and variable length records Master and transaction files File access and organisation methods Sequential file access and update algorithms File security, backup and archiving Data validation and verification

Database Systems

Topic overview Flat files and the relational model Relational and other contemporary database systems Primary, foreign, composite and candidate keys Indexes and links between tables Entity relationship modelling Normalisation to third normal form The database management system, queries and user views

The Operating System

Topic overview The need for an operating system The kernel and process management Memory protection and the backing store The user interface between user and hardware Directory structures and file attributes Utility software Batch, real time control and transaction processing

Algorithms and Programs

Topic overview Defining and designing algorithms Variables, constants and identifiers Scope, subprograms and parameter passing Sequence, selection and repetition Mathematical and logical operations Standard algorithms: sorting, searching and compression Dry running, trace tables and test data

Principles of Programming

Topic overview Procedural programming Event-driven and visual programming Mark-up languages Object-oriented programming: objects, classes and methods High-level languages Low-level languages Choosing a language for a problem

Systems Analysis

Topic overview The systems life cycle and the feasibility study Methods of investigation Analysis, abstraction and decomposition Design and data flow diagrams Testing and changeover Maintenance Backup, recovery and documentation

Software Engineering and Program Construction

Topic overview Integrated development environments and their purpose Editors, syntax highlighting and code entry tools Debugging tools: breakpoints, stepping and watches Translation, source code and object code Lexical analysis and the symbol table Syntax and semantic analysis Code generation and optimisation

Types of Software System

Topic overview Off-the-shelf, bespoke and custom software Open source and proprietary software Computers in weather forecasting Computer aided design and manufacture Robotics in industry Computer generated graphics and animation Expert systems

Practical Programming

Topic overview Designing data structures: fields, records and data types Key fields and methods of access Validation of input data Designing routines with pseudocode Tracing code and test data Prototyping and evaluating a solution Annotated listings and readable code

Data Security and Integrity

Topic overview Dangers of holding files of personal data Levels of permitted access and access control Passwords and authentication Clerical procedures and write-protection Threats to computer systems Malicious and accidental damage to data Contingency planning and disaster recovery

Computing, Society and the Law

Topic overview Social and economic change from computing Computers and the nature of employment The digital divide and cultural change Environmental cost of computing Data protection and freedom of information law The Computer Misuse Act 1990 and computer crime Copyright, surveillance and professional codes

Advanced Data Structures and Logic

Topic overview Arrays in three dimensions Stacks and queues using pointers and arrays Linked lists using pointers and arrays Binary trees using pointers and arrays Hash tables and collision resolution NAND, NOR and Boolean simplification Masking, clearing registers and encryption

Recursion, Sorting and Searching

Topic overview Recursion Quicksort and merge sort Comparing sorting algorithms Big O notation and algorithm complexity Searching and shortest-path algorithms Traversal of data structures Data compression and its efficiency

Programming Paradigms and Translators

Topic overview Functional, declarative and imperative paradigms Classes, methods and object-oriented design Standardisation of computer languages Ambiguity in natural language and unambiguous notation Backus-Naur form and syntax diagrams Compilers, interpreters and assemblers Translation and execution errors

System Design and Human-Computer Interaction

Topic overview The waterfall approach Agile approaches Documentation and when it is produced Contemporary approaches to communicating with computers Natural language interfaces and spoken ambiguity Design review and validation Evaluating a computer based solution

Software Engineering Tools and Professional Practice

Topic overview Software tools for the software engineering process Software packages in systems analysis and specification Software packages in systems design Testing tools and testing strategies Program version management Program libraries and project management tools Codes of conduct and professional behaviour

Advanced Architecture and Assembly Language

Topic overview Components of contemporary architecture Von Neumann and Harvard architectures The fetch-execute cycle in detail Parallel processing and its limits Assembly language and instruction formats Voice input, command and recognition Mobile and wireless networking

Communication Networks and File Organisation

Topic overview Calculating data transfer rates Lowest-cost routing The internet as a global infrastructure Creating, organising and processing files Hashing algorithms Overflow and file reorganisation Choosing an organisation and a route

Number Representation and Floating Point

Topic overview Binary arithmetic Sign and magnitude representation Two's complement Floating point representation Converting between real numbers and floating point Truncation, rounding and accuracy Shifts, overflow and underflow

Databases and Distributed Systems

Topic overview Consistency, redundancy and data independence Relational organisation and normalisation Restructuring data into third normal form Entity relationship modelling Query languages and SQL Validation, verification and the DBMS Big Data, data warehousing and mining Distributed systems and distributed databases

Operating System Management

Topic overview Types of operating system Interrupts and interrupt handling Memory management and partitioning Buffering and data transfer Scheduling and process states Scheduling policies and priorities Evaluating operating system design

Software Systems and Applications

Topic overview The range of software system types Safety related and safety critical systems Computer control and automation The scope of automation in practice Expert systems The internet, intranets and search Selecting and evaluating a software system

Data Security, Cryptography and Attack

Topic overview Integrity problems in online updating The need for cryptography Symmetric and asymmetric techniques Classical ciphers and cryptographic algorithms Comparing cryptographic strength Biometric technologies Malicious software and its vectors Attacks, defence and penetration testing

Advanced Data Structures and Logic

7 subtopics
21 things to know
A2 Unit 3

What Advanced Data Structures and Logic covers

Advanced Data Structures and Logic is examined in A2 Unit 3, Programming and System Development. It covers arrays in three dimensions, Stacks and queues using pointers and arrays, linked lists using pointers and arrays, binary trees using pointers and arrays, hash tables and collision resolution, NAND, NOR and Boolean simplification and masking, clearing registers and encryption.

Where it is assessed

A2 Unit 3

Programming and System Development.

Check the WJEC specification ↗

The 7 subtopics

Each one has its own page.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

How is an AND gate made from NAND gates?

Key term

Explain how a logical operation tests whether a whole number held in a register is even.

Key term

Give an application that suits a three-dimensional array.

Key term

What is a stack?

Key term

What is the head pointer of a linked list?

Key term

What is a binary tree?

Key term

What is a hash table?

Numbers

State the formula for the address of element [i][j][k] of a three-dimensional array stored in row-major order.

Key term

Name the three operations a stack supports and state what each does.

Key term

How is the end of a linked list marked?

Key term

Define the root of a tree.

Key term

What does a hash function do?

Key term

State the truth table of a two-input NAND gate.

Key term

Why can a bitwise operation be applied to a whole register in a single instruction rather than one bit at a time?

Key term

How many nested loops are needed to visit every element of a three-dimensional array exactly once?

Key term

Write pseudocode for the push operation on an array-based stack.

Key term

What is the free list in an array implementation of a linked list?

Key term

What is a leaf node?

Key term

Why is the remainder after division by the table size a suitable basis for a hash function?

Key term

Write the NAND operation in Boolean notation and then apply De Morgan's law to it.

Key term

Which operation and mask force bit 3 of a byte to 1 without disturbing any other bit?

Take Advanced Data Structures and Logic further

The same content, four other ways.

Questions from this topic

Each one with the model answer underneath.

1
What is a three-dimensional array?
Model answer
A three-dimensional array is a static structure holding elements of one type that are located by three subscripts, so it behaves as a stack of two-dimensional tables.
2
How many elements does an array declared with bounds 0 to 2, 0 to 3 and 0 to 4 hold?
Model answer
It holds 3 × 4 × 5 = 60 elements.
3
How is a single element of a three-dimensional array referred to in a program?
Model answer
It is referred to by the array name followed by all three subscripts, such as sales[2][1][4].
4
Give an application that suits a three-dimensional array.
Model answer
Sales figures held by product, by region and by month suit a three-dimensional array, with one subscript for each of the three.
5
Explain how a colour image is held in a three-dimensional array.
Model answer
The first two subscripts give the row and column of the pixel and the third selects the red, green or blue component of that pixel.
6
State the formula for the address of element [i][j][k] of a three-dimensional array stored in row-major order.
Model answer
The address is base + ((i × D₂ + j) × D₃ + k) × w, where D₂ and D₃ are the sizes of the second and third dimensions and w is the width of one element.

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Hardware: Architecture, Memory and Storage

Networks and Data Transmission

Logic Gates and Boolean Algebra

Data Representation and Data Types

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AEncryption is reversible.

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CA hash cannot be reversed.

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A bit is a single binary digit.

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Advanced Data Structures and Logic revision questions

What does Advanced Data Structures and Logic cover in WJEC A-Level Computer Science?: 7 subtopics: arrays in three dimensions, stacks and queues using pointers and arrays, linked lists using pointers and arrays, binary trees using pointers and arrays, hash tables and collision resolution, nand, nor and boolean simplification and masking, clearing registers and encryption. Each one has its own page with questions and model answers.
How is Advanced Data Structures and Logic organised?: By the WJEC 601-5345-3 specification, subtopic by subtopic, so it matches the order you are taught it in.

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